EFFECT OF INTERPHASE, THERMAL INDUCED DISLOCATIONS AND PRESENCE OF VOIDS ON THE FLOW STRESS OF METAL MATRIX NANOCOMPOSITES

EFFECT OF INTERPHASE, THERMAL INDUCED
DISLOCATIONS AND PRESENCE OF VOIDS ON THE FLOW
STRESS OF METAL MATRIX NANOCOMPOSITES



LIN KUNPENG



A THESIS SUBMITTED
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING
NATIONAL UNIVERSITY OF SINGAPORE
2015



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DECLARATION

I hereby declare that this thesis is my original work and it has been written by me
in its entirety. I have duly acknowledged all the sources of information which
have been used in the thesis.

This thesis has also not been submitted for any degree in any university
previously.







Lin Kunpeng
01 June 2015




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i

ACKNOWLEDGEMENTS

First and foremost, I would like to express my utmost gratitude to my supervisors, Dr. Pang Sze
Dai and Prof. Quek Ser Tong, who have supported me throughout my graduate study with their
motivation, enthusiasm and advice while gave me freedom to explore on my own. This work
could not have been completed without their guidance and support. It has been my privilege to
work closely with Dr. Pang Sze Dai and Prof. Quek Ser Tong, I have enjoyed the opportunity to

watch and learn from their knowledge and experience.

I would like to show my appreciation to Dr. Shailendra P. Joshi and Dr. Poh Leong Hien for their
insightful comments and constructive criticisms.

I am deeply grateful to Dr. Elliot Law for his encouragement and practical advice. I am also
thankful to him for reading my draft paper, correcting grammars and commenting on my views.

I would also like to acknowledge the National University of Singapore for supporting me with
Research Scholarship for the entire duration of my study.

I would like to express my warm thanks to my colleagues: Mr. Sixuan Huang, Dr. Yang Zhang,
Mr. Yu Wang, Mr. Ming Luo and Ms. Zhongrui Chen, for their friendship, encouragement and
support.

ii

Last but not least, my heartfelt thanks go to my family, especially my parents Shujing Lin and
Meiting Huang and my wife Xiao Lu, for their unconditional love and support throughout all
these years.

iii

TABLE OF CONTENTS

ACKNOWLEDGEMENTS i
TABLE OF CONTENTS iii
SUMMARY vii
LIST OF TABLES x
LIST OF FIGURES xi

LIST OF SYMBOLS xvi
Chapter 1. Introduction 1
1.1 Background and motivation 1
1.2 Objective 9
1.3 Scope 10
1.4 Organization of Thesis 11
Chapter 2. Literature Review 15
2.1 Interphase in metal matrix composites (MMCs) 15
2.1.1 Experimental results 15
2.1.2 Effect of the interphase 19
2.2 Interphase in metal matrix nanocomposites (MMNCs) 24
2.3 Thermal residual stress in MMCs 27
2.3.1 Experimental results 27
2.3.2 Effect of thermal residual stresses 29
2.4 Thermal induced dislocations in MMCs 31
iv

2.4.1 Existence of thermal induced dislocations 31
2.4.2 Theoretical model of thermal induced dislocations 32
2.4.3 Effect of thermal induced dislocations 34
2.5 Thermal induced dislocations in MMNCs 35
2.6 Void in MMCs 36
2.6.1 Experimental results 36
2.6.2 Effect of void 38
2.7 Void in MMNCs 40
2.8 Analytical model of MMNCs 41
2.9 Numerical simulation of MMNCs 43
Chapter 3. Effects of Interphase on Mechanical Response of MMNCs 45
3.1 Simulation of interphase using level set in extended finite element method (XFEM) 45
3.1.1 Types of discontinuities 45

3.1.2 Introduction to XFEM 48
3.1.3 Level set method 49
3.1.4 Enrichment and selection of enriched nodes 53
3.1.5 Discretization and numerical integration 55
3.1.6 Review discrete dislocation simulation of MMNCs and numerical procedure 60
3.1.7 Comparison with work by original author 69
3.2 Effects of interphase elastic properties 71
3.2.1 Effect of interphase Poisson ratio 71
3.2.2 Effect of interphase Young’s modulus 73
3.3 Effect of interphase thickness 76
v

3.4 Effect of particle volume fraction 77
3.5 Effect of resistance to dislocation motion in the interphase region 81
3.6 Comparison with Mg-ZnO nanoxomposites experimental results 84
3.7 Discussions 88
Chapter 4. Effects of thermal residual stresses and thermal generated dislocation on the
mechanical response of MMNCs 91
4.1 Formulation of thermal stress 91
4.2 Multiple slip systems 93
4.2.1 Multiple slip systems orientations for an idealized fcc single-crystal 94
4.2.2 Formulation of inclined slip systems 95
4.2.3 Implementation of multiple slip systems 102
4.3 Numerical implementation 103
4.3.1 Problem formulation 103
4.3.2 Computation parameters 106
4.3.3 Numerical validation using passivated metal interconnects 107
4.4 Numerical simulation of thermal residual stress in MMNCs 110
4.4.1 Problem formulation 110
4.4.2 Temperature range and cooling rate 111

4.4.3 Material parameters 114
4.5 Results of thermal residual stress in MMNCs 114
4.5.1 Thermal stress and thermal induced dislocation 115
4.5.2 Effect of particle volume fraction 119
4.6 Effect of thermal residual stresses and thermal induced dislocations 122
4.7 Comparison with Mg-ZnO nanoxomposites experimental results 129
vi

Chapter 5. Effects of void on the mechanical response of MMNCs 133
5.1 Modeling of dislocations leaving non-convex domain 133
5.2 Numerical Implementation 139
5.2.1 Problem formulation 139
5.2.2 Computation parameters 141
5.2.3 Numerical validation using a voided single crystal 142
5.3 Numerical simulation of voided MMNCs 144
5.4 Effect of void volume fraction 146
5.5 Effect of void distribution 149
5.6 Effect of lattice orientation 155
5.7 Effect of particle aspect ratio 160
Chapter 6. Conclusions and future work 167
6.1 Conclusions 167
6.2 Recommendations for future work 170
References 173
List of Publications 188


vii

SUMMARY

Metal matrix nanocomposites (MMNCs) have attracted considerable research interest due to
their high strength and stiffness, while retaining much of the ductility of the metallic matrix. Due
to the difficulties in material processing and fabrication, the experimental studies on the effect of
morphology on the mechanical response of MMNCs have seldom been reported. On the other
hand, numerical simulations can be carried out with greater ease and the effects of shape, size
and distribution of particles have been reported in literature. In particular, the discrete dislocation
approach has successfully simulated the trend of increasing flow stress and degree of hardening
with nano-particles. However, the existing discrete dislocation approach has ignored the
presence of interphase regions, thermal residual stress and void, which are important features
that are present in the MMNCs after processing. The objective of is to this study investigate
these features in MMNCs using numerical simulation and determine their effects on overall
mechanical response of these materials.

By using level set in XFEM, interphases regions are introduced into the numerical model. The
simulations show that impediment of dislocation motion by the particles and the load-bearing
effect are the two dominant strengthening mechanisms in MMNCs. When the interphase
thickness is small (half the particle radius or smaller), the elastic properties of interphase do not
have significant effect on the overall response of MMNCs. An increase in the particle volume
fraction, the young’s modulus and the resistance to dislocation motion of the interphase result in
a significant increase in the flow stresses. The simulations of MMNCs shows that by including
interphase regions in the simulation, one can obtain a more accurate estimate of the overall
viii

response.

The development of thermal residual stresses and thermal induced dislocations in MMNCs are
predicted using discrete dislocation simulation. The effect of thermal residual stresses and
thermal generated dislocation on the overall response is investigated by applying in-plane shear
on a unit cell after the thermal cooling process. The simulations show that thermal residual
stresses in MMNCs are high enough to generate thermal induced dislocations. Dislocation

density is higher around particles compared to the rest of the matrix. Under applied shear
deformation, new generated dislocations are likely hindered by thermal induced dislocations and
form pile-ups. Consequently, the flow stress and degree of hardening are higher when thermal
residual stresses are included in the simulations. By considering thermal residual stresses in the
model, the predicted mechanical behavior of the MMNCs can match with experimental results
better.

By using level set method in XFEM, the void is simulated as an inclusion with a Young’s
modulus 1000 times lower than the matrix. Image stresses due to dislocations reach the surface
of the void are computed by embedding the discontinuities in the finite element solution.
Simulation results show that the stiffness, yield stress and flow stress of MMNCs decrease with
increasing void content when the void is fixed at the center of the unit cell. Under 2 % tensile
strain, the difference of flow stress can be as much as 32 % with different void distribution,
which suggests that the volume fraction of the void itself is not sufficient to estimate the strength
of voided MMNCs. The change of lattice orientation can also induce a 37 % change in flow
stress at 2 % tensile strain. Moreover, current results show that flow stress in voided MMNCs
ix

increases with decreasing particle aspect ratios.

x

LIST OF TABLES

Table 1.1 Room temperature mechanical properties of Mg and composites samples (Hassan and
Gupta, 2006). 4
Table 2.1 Elastic modulus, in form E/(1-v2), for matrix, interphase, and particles in composites
(Das et al., 1997). 18
Table 2.2 Values of the measured and theoretical density and porosity (%) for the pure copper
and 1-Pass, 4-Pass and 8-Pass. 37

Table 4.1 Tensile material properties for 6061 Al. 112
Table 4.2 Elastic and CTE properties used for 1100-O Al. 113
Table 4.3 Different material properties in MMNCs with different particle volume fractions under
thermal residual stress. 122
Table 5.1 Change in yield stress with different void volume fraction. 149


xi

LIST OF FIGURES
Fig. 2.1 Qualitative analysis of the interphase intermetallic-aluminium alloy. Top, atomized
intermetallic; bottom, mechanical alloying (MA) intermetallic (Torralba et al., 2002). 17
Fig. 2.2 Pole debonding and equator debonding. 21
Fig. 2.3 Representative micrographs showing reinforcement distribution of Y
2
O
3
particulates and
presence of nanopores in the case of (a) Mg/0.17Y
2
O
3
and (b) Mg/0.7Y
2
O
3
(Tun 2009). 41
Fig. 3.1 Different categories of continuities (Mohammadi, 2003). 46
Fig. 3.2 Sketch of one-dimension bi-material bar. 47
Fig.3.3 Two-dimension bi-material problem. 47

Fig.3.4 Signed distance level set function φ. 50
Fig. 3.5 Circular level set function 52
Fig. 3.6 Selection of enriched nodes for circular interface; nodes marked by circles are enriched.
56
Fig. 3.7The sub-triangles associated with elements cut by interface. 60
Fig. 3.8 Decomposition of problem for dislocation body with inclusions into problem of
interacting dislocations in the homogeneous finite solid and the complementary problem for the
non-homogeneous body without dislocations (Van der Giessen and Needleman, 1995) 62
Fig. 3.9 Two-dimensional unit cell with distributed particles (shaded elements), Frank-Read
sources (squares) and obstacles (circles). 66
Fig. 3.10 Computational procedure for discrete dislocation simulation of MMNCs (Law, 2011).
67
Fig. 3.11 Computational procedure for discrete dislocation simulation of MMNCs with
interphases 68
Fig. 3.12 Underformed configuration of unit cell with location of the discontinuities (marked
with circles) and enriched nodes (marked with ‘×’). 70
Fig. 3.13 Overall response of MMNCs with (current simulation) and without (Law, 2011)
interphases subjected to simple shear. 71
xii

Fig. 3.14 Overall response of MMNCs with different interphase Poisson ratio. Each curve bases
on the average value of 4 realizations. 72
Fig. 3.15 Effect of interphase Young’s modulus for 




 and 

: (a) overall

response of MMNCs; (b) evolution of

 74
Fig. 3.16 Effect of interphase thickness for 




 and 

: (a) overall response of
MMNCs; (b) evolution of

. 78
Fig. 3.17 Effect of particle volume fraction with interphase region for 




 and 





: (a) overall response of MMNCs; (b) evolution of

. 79
Fig. 3.18 Effect of particle volume fraction without interphase region on the overall response of
MMNCs (Law, 2011) 80

Fig. 3.19 Effect of resistance to dislocation motion in interphase region for




 and


: (a) overall response of MMNCs; (b) evolution of

 83
Fig. 3.20 Comparison numerical predictions for Mg-ZnO nanocomposite with absence of
interphase regions and experimentally obtained shear response for 0%, 0.5% and 1.5% of ZnO.
87
Fig. 3.21 Comparison between numerical predictions for Mg-ZnO nanocomposite with
interphase regions and experimentally obtained shear response for 0%, 0.5% and 1.5% of ZnO.
88
Fig. 3.22 Overall response of MMNCs with different interphase Young’s modulus and 50nm
interphase thickness. 90
Fig. 4.1Schematic of dislocation motion on fcc slip planes when crystal is oriented with [110]
parallel to X
3
direction. Because of symmetry and when X
3
direction is very long, the slip mode
is such that dislocations can be idealized as three pairs of straight ed edge dislocations as shown
by ⊥ symbols (Nicola et al., 2004). 95
Fig. 4.2 Sign convention for slip plane and dislocation orientations. 96
Fig. 4.3 s-t coordinate system and x-y global coordinate system. 100
Fig. 4.4(a) Geometry of line model. (b) Decomposition of unit-cell problem into thermo-elastic

problem and plastic relaxation problem (Nicola et al., 2004) 104
Fig. 4.5 Undeformed configuration of line model with element size of 50 nm. (a) h/w=1, (b)
h/w=0.5. 107
xiii

Fig. 4.6 Average σ
11
in the line versus imposed temperature for the line with aspect ratio h/w=1.
Element size of mesh 1, mesh 2 and mesh 3 are 100nm, 50nm and 25nm, respectively. 108
Fig. 4.7 Average σ
11
in the line versus imposed temperature for line with aspect ratio h/w=0.5.
Element size of mesh 1, mesh 2 and mesh 3 are 100nm, 50nm and 25nm, respectively. 109
Fig. 4.8 (a) Two-dimensional unit cell with distributed particles (shaded elements), Frank-Read
sources (squares) and obstacles (circles); (b) 2D unit cell model subjected to simple shear. 111
Fig. 4.9 Undeformed shape with particle volume fraction 

. Particles are filled in black,
while Frank-Read sources and obstacles are marked with squares and circles, respectively. 116
Fig. 4.10 Final dislocation structure with particle volume fraction 

. Positive
dislocations and negative dislocation are marked with ‘+’ and ‘×’, respectively. Shaded elements
highlight the regions around particles. 116
Fig. 4.11 Average σ
h
in matrix versus imposed temperature. 118
Fig. 4.12 Dislocation density versus imposed temperature. 118
Fig. 4.13 Average σ
h

in particles versus imposed temperature. 119
Fig. 4.14 Stress σ
h
distribution at 300 K. 120
Fig. 4.15 Average σ
h
in interfacial regions versus imposed temperature with different particle
volume fractions 121
Fig. 4.16 Dislocation density versus imposed temperature with different particle volume
fractions 121
Fig. 4.17 (a) Distribution of dislocations for case without thermal residual stresses under 0.05%
shear strain, 

; (b) distribution of dislocations for case with thermal residual stresses
under 0.05% shear strain, 

 (thermal induced dislocations are marked with blue color
and new generated dislocation are marked with red color). 125
Fig. 4.18 Evolution of dislocation density under shear deformation for cases with or without
thermal residual stresses,

. 125
Fig. 4.19 (a) Distribution of dislocations for case without thermal residual stresses under 0.6%
shear strain, 

; (b) distribution of dislocations for case with thermal residual stresses
under 0.6% shear strain, 

. 126
xiv

Fig. 4.20 Effect of thermal residual stresses on overall response of MMNCs with different
particle volume fraction. 128
Fig. 4.21 Comparison between numerical predictions for Mg-ZnO nanocomposite with absence
of thermal residual stresses and experimentally obtained shear response for 0%, 0.5% and 1.5%
of ZnO. 131
Fig. 4.22 Comparison between numerical predictions for Mg-ZnO nanocomposite with thermal
residual stresses and experimentally obtained shear response for 0%, 0.5% and 1.5% of ZnO. 131
Fig. 4.23 Comparison numerical predictions for Mg-ZnO nanocomposite with inclusion of
thermal residual stresses and interphase regions, and experimentally obtained shear response for
0%, 0.5% and 1.5% of ZnO. 132
Fig. 5.1 Intersection of the slip plane with the domain. (a) Convex domain; (b) Non-convex
domain 134
Fig.5.2 Problem decomposition for convex domain. The problem in the center is posed on an
infinite domain with dislocations in it. The problem on the right is on the original domain , but
the imposed tractions and displacement boundary conditions are corrected. The three problems in
the figure will be denoted problems , 

and 

, respectively (Romero et al., 2008). 135
Fig. 5.3 Problem decomposition including the slip across the plane. The complete problem with
discontinuities reaching the boundaries is approximated by the sum of three simpler problems.
The four problems will be referred to, from left to right, as , 

, 

and 

, respectively (Romero

et al., 2008). 136
Fig. 5.4 Geometry of a voided single crystal. 140
Fig. 5.5 Initial configuration of voided single crystal with distributed Frank-Read sources (blue
squares). 142
Fig. 5.6 Overall responses of voided single crystal under uniaxial tension. Dash curves in (a), (b)
and (c) are results of three realizations in current works while solid black curves are results from
Segurado and Llorca (2009). 143
Fig. 5.7 Dislocation structures at 2% tensile strain in voided single crystal. (a) Result from
current simulation. (b) Result from Segurado and Llorca (2009). Green upward-pointing and red
downward-pointing triangles represent positive and negative dislocations, respectively. Crosses
in (b) stand for dislocation sources. 144
Fig. 5.8 Two-dimensional unit cell with multiple particles (shaded elements), a void (a blue
circle) and dislocation sources (squares). 145
xv

Fig. 5.9 Effect of void volume fraction for 

: (a) Overall response for 0 to 2% tensile
strain; (b) Overall response for 0 to 0.2% tensile strain. 147
Fig. 5.10 Dislocation structures at 2% tensile strain: (a), (b), (c) and (d) are cases with 0%, 1%, 3%
and 5% void content, respectively. Green upward-pointing and red downward-pointing triangles
represent positive and negative dislocations. Blue circles mark the void area while shaded
elements represent particles. 150
Fig. 5.11 MMNC with varying distribution for 5% void under tensile strain of up to 2%. (a)
tensile stress response (b) evolution of dislocation density. 152
Fig. 5.12 von Mises stress contour of unit cell with different void distributions at 0.08% tensile
strain (a) 

 (b) 


 (c) 

 and (d) 

. 153
Fig. 5.13 Stress-strain curves for different void distribution with tensile strain from 0 to 0.2%.
154
Fig. 5.14 Scheme of voided MMNCs with three slip systems. System (I) and (III) form angles of
54.75
o
and -54.75
o
with respect to system (II). 155
Fig. 5.15 (a) Overall response for different lattice orientations with tensile strain from 0 to 2%. (b)
Evolution of dislocation density. 158
Fig. 5.16 Dislocation structures at 2% tensile strain, (a), (b), (c) and (d) are case 

,


, 

and 

, respectively. 159
Fig. 5.17 Scheme of undeformed configurations with different particle aspect ratios. (a) Aspect
ratio = 1; (b) Aspect ratio = 2; (c) Aspect ratio = 4. 161
Fig. 5.18 (a) Overall response for different particle aspect ratios with tensile strain from 0 to 2%.
(b) Evolution of dislocation density. 162
Fig. 5.19 von Mises stress contour of 0.08% tensile strain. (a) Aspect ratio = 1; (b) Aspect ratio =

2; (c) Aspect ratio = 4. 164
Fig.5.20 Dislocation structures. (a) Aspect ratio = 1, 0.8% strain; (b) Aspect ratio = 1, 2% strain;
(c) Aspect ratio = 2, 0.8% strain; (d) Aspect ratio = 2, 2% strain; (e) Aspect ratio = 4, 0.8% strain;
(f) Aspect ratio = 4, 2% strain. 165


xvi

LIST OF SYMBOLS

 Additional displacement tensor or vector
 Matrix relating strains to displacements
 Bulk modulus, drag coefficient for dislocation motion
 Burgers vector
 The matrix relating stresses to strains
 Young’s modulus
 Force vector, force component, volume fraction
 Height of unit cell
 Stiffness matrix
 Distance, length
 Element shape function matrix
 Unit tangent vector
 Unit normal vector
 Radius
 Distance or position along local horizontal axis
 Temperature, Distance or position along local vertical axis


Cooling rate
 Distance or position along local vertical axis, time or time duration

 Strain energy
 Displacement tensor or vector, displacement component
xvii

 Width of unit cell
 A two-dimensional point
 Thermal expansion coefficient
 Surface or boundary


Shear deformation rate
 Applied shear strain
 Strain tensor or vector, strain component
 Nodal level set values
 Angle or orientation with respect to horizontal axis
 Shear modulus
 Density
 Stress tensor or vector, stress component
 Shear stress, strength
 Poisson’s ratio, glide velocity of dislocation
 Angle or orientation with respect to horizontal axis
 Discontinuous enrichment function
 Level set function
 Domain


Symmetric gradient operator
xviii

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1

CHAPTER 1. INTRODUCTION

1.1 Background and motivation

When a reinforcement phase is dispersed within a continuous metallic host material, it is called
metal matrix composite (MMC). Particle-reinforced metal matrix composites have been
extensively used in mechanical engineering as structural and/or functional materials, in particular
aluminum-matrix composites. The purpose of the particle is to improve the thermo-mechanical
properties and performance of the host metal (Callister, 2003). For example, the addition of
particle may improve specific stiffness, specific strength, creep resistance, thermal conductivity
and dimensional stability. However, the presence of the particulate decreases the composite
ductility and fracture toughness dramatically, which limits the structural applications of such
composites in, for example, the aerospace and automotive industries (Su et al., 1999). This leads
to the development of metal matrix nanocomposites (MMNCs).

Nanomaterials in general can be classified into two categories: (a) nano-structured material
where the characteristics length of the microstructure, e.g. grain size of a polycrystalline
material, is in the nanometer range; and (b) nano-sized structural element where at least one of
the overall dimensions of a structural element is in the nanometer range (Paliwal and Cherkaoui,
2012). Recent advances in nanotechnology have led many investigations devoted to nanoscale
science and to the development of various nanomaterials e.g. nanocomposites and nano-scale
2

multilayer laminates (Benkassem et al., 2008; Demkowicz et al., 2008; Li et al., 2010). These
nanomaterials are extremely interesting because they exhibit unusual mechanical,
thermomechanical, electrical, optical and magnetic properties as compared to conventional
composites or laminates of similar constituents, volume proportion and shape/orientation of
reinforcement (Paliwal and Cherkaoui, 2012).

MMNCs, which can be defined as MMCs reinforced with nano-sized fillers, show significant
promise for use as structural and/or functional materials. The reason is many experimental results
shown that reducing the size of particles to the nanoscale dramatically increases the mechanical
strength of MMCs while preserving good ductility (Cao et al., 2008). However, due to their high
specific surface area and poor wettability, nano-size particles in metal matrix composites tend to
agglomerate into coarse clusters even at very low particle content (Tjong, 2007), leading to little
further improvement in the mechanical properties beyond a few volume percent of particles.
Furthermore, controlling the sizes of nano-particles is still difficult during manufacture. Hence,
current experimental studies have mainly focused on developing and improving various methods
to achieve good dispersion of nano-size particles in metal matrix composites (Tjong, 2008); few
have explored the effects of particle size, geometry and distribution as well as mechanisms and
processes which govern the response and mechanical behavior of MMNCs.

In the view of difficulties faced in experimental work, numerical simulation can be extremely
useful for studying the properties of MMNCs, e.g. Law et al. (2011 and 2012) conducted a two-
dimensional multiparticle representative volume element (RVE) simulation using discrete
dislocation method to investigate the mechanical properties of MMNCs. The trends of increasing
3

flow stress and degree of hardening with lager particle volume fraction and smaller particle size
in MMNCs are successfully demonstrated in the simulations considering two phases, the matrix
and the reinforcements (Law, 2011).

However, the improvements of the mechanical responses reported in experiments are more
significant than those shown in simulations especially at very low particle volume fractions.
Furthermore, the simulations show that the elastic properties of the particles relative to the
matrix do not have a considerable effect on the mechanical properties of the resulting
nanocomposites. This phenomenon suggests that different MMNCs with the same type of matrix
but different kinds of particles have similar mechanical properties, which does not match the

experimental results. Those results reported by Hassan and Gupta (2006), show that the type (i.e.
chemical composition) of reinforcing particles results in different degrees of strength and
ductility improvements compared to the pure metallic matrix. Hassan and Gupta (2006) reported
that alumina nanoparticles result in greater improvement on 0.2% yield strength (YS) and
ultimate tensile strength (UTS) of magnesium nanocomposite compared to zirconia nanoparticles
(shown in Table 1.1). They suggest that this is because the former are more susceptible to
diffusion controlled superficial reaction with magnesium to form strong interfacial bonding. In
addition, under the current numerical model, some features like interphase, thermal residual
stress and porosity, which may significantly affect the mechanical properties of MMNCs, have
not been considered. These discrepancies indicate that there are other predominant strengthening
mechanisms which should be considered in the simulations and the current numerical model
needs to be modified to get a more realistic simulation of mechanical behavior of MMNCs.